A recent article in FORE
Magazine (“A Perfect Match,” November/December 2013) argues the Handicap
System makes for “perfect “competition even when players compete from different
tees. You can trace the push for Sec. 3-5 (Sec. 8-4f back in 1990) to Alice Dye
and her article “Tees for Two or More” in the July 1990 PGA Magazine. Ms. Dye, like
the article, used an example of individual stroke play to demonstrate the
equity of Sec. 3-5. If a competition is
social (e.g., husband v. wife, buddy v. buddy) stroke play, Sec. 3-5, while not
perfect, is good enough. The problem
comes when the competition is more serious and when other forms of competition
are introduced. Articles like this can unintentionally
mislead the reader into believing Sec. 3-5 cures all of the equity problems of
such competition. I believe the use of Sec. 3-5 should be
discouraged and only used as a last resort.
Here are some reasons why:
1. Biased Handicaps - Rounding errors and the Bonus for
Excellence can give one player an advantage when competition is from different
tees. The Appendix presents an example
of two players with 13.5 indexes. When
they play from different tees, one player has an expected net score 1.7 strokes
below that of his competitor. Based on
certain assumptions, that player should win 65 percent of the time. Had they played from the same tees, neither
player would have an advantage.
2. Equity of Competition – Sec. 3-5 depends upon the
accuracy of the Course and Slope Ratings. The standard error of the estimate of
Course and Slope Ratings is much larger than the USGA wants to admit. Given these error, the efficacy of Sec. 3-5
becomes in doubt. Significant errors can
occur in assigning the proper handicap when a player establishes his index
playing one set of tees, but plays another set of tees in a competition.
3. Misuse of Sec. 3-5
– I have seen Sec. 3-5 applied to various forms of competition –scrambles,
Chapman, foursome, and four-ball. I have
not seen any evidence indicating Sec. 3-5 makes for equitable competition in
these formats. I have conducted small
sample studies that show Sec. 3-5 did not always equalize competition in scramble and four-ball events. To be fair, the USGA does not recommend using
Sec. 3-5 for scramble competitions, but it also does not explicitly prohibit
its use. When Sec. 3-5 is used in a four-man scramble,
the handicap allowances for the C and D players are often the same from both
the front and back tees. The team that recognizes this anomaly, and places it C
and D players on the front tees has a significant advantage.
4. Handicap Stroke Allocation Issue – All the theory behind
stroke allocation goes out the window when players compete from different
tees. This is not a great concern,
because I do not believe stroke allocations are a major determinant in who wins
a match. Advocating competition from
different tees, however, sends the message that Section 17 (Allocation of
Handicap Strokes) of the USGA Handicap
System isn’t all that important.
5. Pace of Play – One
of the arguments for “Play It Forward” is that rounds would be played
faster. When players compete from
different tees in the same foursome, it takes longer to play a round and any time
benefit from Play it Forward could be
lost.
6. Smaller Scoring Variance from the Front Tees - In some four-ball competitions, the second ball is used as a tie-breaker. It is probable the scoring variance is smaller from the front tees. This should give the team playing the front tees a small edge when the second ball is used as a tie-breaker.
6. Smaller Scoring Variance from the Front Tees - In some four-ball competitions, the second ball is used as a tie-breaker. It is probable the scoring variance is smaller from the front tees. This should give the team playing the front tees a small edge when the second ball is used as a tie-breaker.
Appendix
Section 3-5 (Players
competing from different tees) argues competition would be equitable if the
difference in Course Ratings is added to the handicap of the player competing
from the tees with the higher course rating.
Applying Section 3-5, however, introduces three possible errors
1. Rounding the Difference in Course Rating Error – To
demonstrate the equity of Sec. 3-5, examples are manufactured to give both
players the same net score. The example shown in Table 1 is taken from the USGA
explanation of Sec. 3-5. Both players
have an expected net score of 71, and equity is allegedly assured.
Table 1
USGA’s 3-5 Procedure
Gary (Gold Tees)
|
Vs.
|
Bob (Blue Tees)
|
10.4
|
Index
|
10.4
|
130/113
|
X Slope Rating/113
|
140/113
|
12
|
Course Handicap
|
13
|
71.1
|
Course Rating
|
73.2
|
83
|
Target Score
|
86
|
12
|
Adjusted Handicap
|
13 + 2 =15
|
71
|
Net Score
|
71
|
The findings, however, depend upon the choice of the Course
Ratings. Table 2 demonstrates that
changing the Course Ratings can lead to different results.
Table 2
3-5 with Different Course Ratings
Gary (Gold Tees)
|
Vs.
|
Bob (Blue Tees)
|
10.4
|
Index
|
10.4
|
130/113
|
X Slope Rating/113
|
140/113
|
12
|
Course Handicap
|
13
|
71.4
|
Course Rating
|
73.8
|
83
|
Target Score
|
87
|
12
|
Adjusted Handicap
|
13 + 2 =15
|
71
|
Net Score
|
72
|
In Table 2, the Net Scores of the two players are not
equal after making the Sec. 3-5 adjustment.
The difference is due to rounding the difference in Course Ratings. Therefore, competition is not as perfect as
the article implies.
2. Bonus for
Excellence Error - For equity, however, it is not the target score that is
important, but a player’s expected net score.
Ideally, the expected net score of both competitors should be the
same. For simplicity, we assume a
player’s expected gross score is the average of his ten best out of twenty
scores.[1] A player’s expected gross score is given by
the handicap formula:
Expected
Gross Score = (Index · (Slope Rating/113))/.96 + Course Rating
The .96 in the equation is the Bonus for Excellence.
A player’s handicap is:
A player’s handicap is:
Handicap
= Index · (Slope Rating)/113
A player’s Expected Net Score is:
Expected
Net Score = Expected Gross Score – Handicap
= (Index· (Slope
Rating/113)/.96 + Course Rating - Index · (Slope Rating/113)
= 0.04· (Index · Slope
Rating)/113 + Course Rating
When the Slope Ratings of the two tees are fairly close, the
Bonus for Excellence introduces only a minor error. This is not always the case, however. As an example, assume two payers have an
index of 13.5. One player plays the gold
tees with a Slope Rating of 88. The other player plays from the blue tees with a Slope Rating of 146. The player
from the gold tees would have an expected net score .4 strokes over the Course
Rating. The player competing from the
blue tees would have an expected net score .7 strokes over the Course
Rating. The player competing from the
gold tees will have a slight edge (.3 strokes) that will not be corrected by
Section 3.5. (Note: This bias is due to the USGA’s Bonus for Excellence which
is yet another argument for its elimination.[2] The bias favors the player with the lower
handicap, and not necessarily the player with the lower index. This is contrary to the intent of the Bonus
for Excellence that supposedly rewards the better player.)
3. Handicap Rounding Problem – When players
with the same index play from the same tees any rounding error is the same for
both players. When they play from
different tees, rounding can give one player up to a 1-stroke advantage. Let’s use the example above The unrounded handicap of the player playing
the gold tees would be 10.51. The
unrounded handicap for the player competing from the white tees would be
17.44. The difference in unrounded
handicaps is 6.93 strokes or approximately 7 strokes. The difference in their rounded handicap,
however, is 6 strokes. In this case the
player competing from the gold tees gains a 1-stroke advantage because of
rounding.
Table 4 also shows how the errors can affect the probability that a player wins a match. It is assumed that
each player’s scoring record has standard deviation of 3.0. In the extreme case, the probability of winning can reach .65. In this instance, playing from different tees has
made the competition less equitable.
Table 4
Probability of Gold Tee Player Winning[4]
Bias
|
Net
Score Advantage
|
Probability
of Winning
|
Bonus for Excellence (BE)
|
.3
|
.53
|
BE + Course Rating
Rounding(CRR)
|
.3 + .4 = .7
|
.57
|
BE + CRR + Handicap Rounding
|
.3 + .4 + 1.0 = 1.7
|
.65
|
[1] A
player’s actual expected score, under certain assumptions, is the average of
his ten best scores plus .8 times a player’s scoring variance. If both player’s have the same variance, the
average of a player’s ten best scores is an adequate proxy for his actual
expected score for the purposes here.
[2]
Dougharty Laurence, “The USGA’s Bonus for Excellence Ruse,”
www.ongolfhandicaps.com, January 15, 2013
[3]
There will still be rounding problems when players play from the same
tees. The example was a special case
where the indexes of both players were the same.
[4]
The methodology behind the estimates can be found in “A Sandbagger’s Guide to
Winning,” www,ongolfhandicaps.com, December 19, 2013
